SSF is a system to discover the structure of simultaneous equations governing an objective process through experiments. SSF combined with another system SDS to discover a quantitative formula of a complete equation derives the quantitative model consisting of simultaneous equations reflecting the first principles underlying in the objective process. The power of SSF comes from the use of the complete subset structure in a set of simultaneouls equations which can be experimentally identified. The theoretical foundations of the structure identification and the algorithm of SSF are described, and its efficiency and practicality are demonstrated and discussed with large scale working examples. This work is to promote the research of scientific discovery to a novel and promising direction, since the conventional equation discovery systems could not handle such a simultaneous equation process.

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